Question

An iron bar having young modulus \[{{10}^{11}}N/{{m}^{2}}\] and coefficient of linear expansion, c. It is 1m long and \[{{10}^{-3}}{{m}^{2}}\] in area is heated from 0 \[{}^\circ C\] to 100 \[{}^\circ C\]. Find the compressive force in newton developed inside the bar.

Answer 1

Hint: When a solid is heated it gets expanded. Also upon application of force a solid may get extended and may shrink in length.

Complete step by step answer:
Given quantities are
F=?
\[\gamma \]=\[{{10}^{11}}N/{{m}^{2}}\]
\[{{10}^{11}}N/{{m}^{2}}\]
A=\[{{10}^{-3}}{{m}^{2}}\]
Initial temperature=\[{{T}_{i}}\]=0\[{}^\circ C\]
Final temperature=\[{{T}_{\begin{smallmatrix}
 f \\

\end{smallmatrix}}}\]=100\[{}^\circ C\]
Change in temperature=\[{{T}_{\begin{smallmatrix}
 f \\

\end{smallmatrix}}}\]-\[{{T}_{i}}\]=\[\Delta T\]=100 \[{}^\circ C\]
Using the formula, \[F=AY\alpha \Delta T\]
We get, F=\[{{10}^{-3}}\times {{10}^{11}}\times {{10}^{-6}}\times 100\]
F=10000 N

Additional Information:
When a force is applied on a body, it acts upon a certain area of contact and it, in turn, produces stress. In the physics force applied per unit, the area is called stress. When a force is applied it can either compress a material or it can extend its length. The extent of such stretch or compression is given by Strain. The strain is defined as the ratio of change in length to the original length. Every material responds uniquely to stress. If a force changes the length, then the extent of change is calculated with the help of modulus of elasticity called young’s Modulus. Young's modulus is a number that measures the resistance of a material to oppose the change in its length. It is named after the 17ᵗʰ century physicist Thomas Young.

Note:
This is an example of mechanical properties of solids upon application of force. When a force is placed on a material, the material stretches or compresses in response to the force.